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Let $N$ be a compact Riemannian manifold. A quasi-harmonic sphere on $N$ is a harmonic map from $(ℝ^{m}, e^{{| x |}^{2} / 2 (m - 2)} / d s_{0}^{2})$ to $N$ ( $m \geq 3$ ) with finite energy ([LnW]). Here $d s 2_{0}$ is the Euclidean metric in $ℝ^{m}$ . Such maps arise from the blow-up analysis of the heat flow at a singular point. In this paper, we prove some kinds of Liouville theorems for the quasi-harmonic spheres. It is clear that the Liouville theorems imply the existence of the heat flow to the target $N$ . We also derive gradient estimates and Liouville theorems for positive...

Displaying 1 – 11 of 11

Lefschetz theorems for the integral leaves of a holomorphic one-form

Lewy's theorem fails in higher dimensions.

Linear Growth Harmonic Functions on Complete Manifolds with Nonnegative Ricci Curvature.

Linear $\infty$ -harmonic maps between Riemannian manifolds.

Liouville theorem for harmonic maps with potential.

Liouville theorems for exponentially harmonic functions on Riemannian manifolds.

Liouville theorems for harmonic maps.

Liouville theorems for self-similar solutions of heat flows

Local solvability of a constrained gradient system of total variation.

Locally Minimizing Harmonic Maps from Noncompact Manifolds.

Long-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid.

Currently displaying 1 – 11 of 11